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Math Help - Finding solutions for trig equations

  1. #1
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    Finding solutions for trig equations

    Im sure this is a trivial problem for many, but not having done this for a while im a bit rusty and cant figure it out

    I have the answers to the following question, but i do not know how to calculate them from the first:

    Find all the solutions to the following equation

    Sin( ((5x)/2) + 15) = 0.34

    Where 0≤x≥360

    The answers are (1.950749625,58.04925038,145.9507496,202.0492504,2 89.9507496,346.0492504)

    My attempt

    sin-1(0.34)=19.88

    19.88-15 = 4.88

    (4.88*2)/5 = 1.95

    How are the other answer worked out from here?

    Any input appreciated

    Thanks
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  2. #2
    MHF Contributor ebaines's Avatar
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    Re: Finding solutions for trig equations

    Remember that there are two quadrants where sin(x) = 0.34 (both first and second quadrant), so x may be either 19.88 degrees or 180 -19.88 = 160.12 degrees. And furher since the final answer must be in the range 0 < x < 360, that means that 5x/2+15 will be in the range 15 to 915 degrees. Which means in addition to 5x/2= 19.88 you also have 5x/2=19.88 + 360 and 5x/2+15 = 19.88+ 2x360 degrees. Same with 5x/2+15=160.12, 5x/2+15= 160.12+360, etc.

    One other comment - no fault of yours given the answers in the form that that you were given, but it drives me crazy to see answers taken out to 10 decimal places of accuracy when the data you were given is only two decimal places. The proper answer for the first one is x=1.95, not x= 1.950749628.
    Last edited by ebaines; October 22nd 2012 at 08:12 AM.
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  3. #3
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    Re: Finding solutions for trig equations

    Thanks, that sorted the problem. Do you know how i would rearrange cos(56deg -3x) = -0.305. iv tried to work this out as inverse of cos 107.758 then use (107.758-56)/-3 which gives me the wrong answers, i also tried to get the other cos angle as 107.758-90 = 17.758 then staying in the negative quadrant of cos 270 + 17.758 = 287.758 to which iv got the wrong answers

    Thanks
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  4. #4
    MHF Contributor ebaines's Avatar
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    Re: Finding solutions for trig equations

    Quote Originally Posted by MMCS View Post
    Do you know how i would rearrange cos(56deg -3x) = -0.305. iv tried to work this out as inverse of cos 107.758 then use (107.758-56)/-3 which gives me the wrong answers,
    I think it gives the correct answer of x = -17.25 degrees. What have you been told is the answer?

    Quote Originally Posted by MMCS View Post
    i also tried to get the other cos angle as 107.758-90 = 17.758
    Remember for that cos(x) = cos(-x) = 360 - cos(x). So try -107.8 degrees, which is the same as +252.2 degrees.
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  5. #5
    Senior Member MaxJasper's Avatar
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    Lightbulb Re: Finding solutions for trig equations

    Inspect roots before finding their numerical values (Radian):

    Attached Thumbnails Attached Thumbnails Finding solutions for trig equations-sin-2.5x-15-0.34-roots.png  
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